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    2017-Ole_Witt-Hansen-Examples Of Differential Equations In Physics
    This is an article from the author’s homepage. The work contains fundamental and basic background and derivation of the differential equation models for a number of phenomena.

    Keywords: projectileair resistancefree falldragharmonic oscillation

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    2002-Chai-Optimal initial angle to fire a projectile
    Assume a projectile is fired without air resistance and lands at a height y above its initial vertical position. What is the optimal initial angle of firing to maximize the horizontal distance...

    Keywords: optimizationprojectile motionlaunch angle

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    3-033-S-TimeUpTimeDown-ModelingScenario
    We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.

    Keywords: projectile motionapexvertical motion

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    3-101-SpringMassFirstTry-NoResistance-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with no damping.

    Keywords: frequencymassoscillationundampedspring constantspring\Single Degree of Freedom System

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    3-102-SpringMassDamped-ModelingScenario
    Students build a model based on their perceptions of what the solution should look like for a simple spring mass system with damping.

    Keywords: frequencymassoscillationstiffnessspring constantspring\dampedSingle Degree of Freedom Systemcoefficient

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    3-020-ChordPathTime-ModelingScenario
    Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is...

    Keywords: Unit CirclepathfallinggravitychordNetwon's Second Law of Motion

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    5-014-TwoSpringMass-ModelingScenario
    We ask students to build a Free Body Diagram for a vertical two mass situation in which the two masses are held fixed at the tip and at the bottom. The mass holds the springs together at the join...

    Keywords: massspring mass dampersprings

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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of...

    Keywords: resistanceprojectile motionprojectilefluidMersenne

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    1-008-HangTime-ModelingScenario
    We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the...

    Keywords: gravityhang timNewton's Second Law of Motionjump shot

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    1-047a-CondensationOptimization-ModelingScenario
    We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top...

    Keywords: simulationdataoptimizationenergycondensationbest fitcostsum of scquare errors

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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction....

    Keywords: population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts

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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring...

    Keywords: energymass-spring systemkinetic energypotential energytotal energy

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    2015-Pendrill-Eager-Free fall and harmonic oscillations analyzing trampoline jumps
    In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes.

    Keywords: Accelerometersfree falljumptrampoline

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    3-045-RampBounce-ModelingScenario
    Students build two projectile motion models (1) a one-dimensional model for a vertically falling ball from a fixed distance until it hits an inclined ramp and (2) a two-dimensional projectile...

    Keywords: projectile motioninclined rampcoefficient of restitutionoptimal anglebounce

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    1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall
    This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern...

    Keywords: parameter estimationdata collectionresistancefallingterminal velocityNewton's Second Law of Motionshuttlecock

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    1-047-Condensation-ModelingScenario
    We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and...

    Keywords: simulationsum of square errorscondensationbest fit

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    3-090-OneSpringMass-ModelingScenario
    We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their...

    Keywords: undampedsum of square errorsmass springHooke's Lawoscilationleast-squares approximation

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    3-140-TwoSpringsOneMassFixedEnds-ModelingScenario
    Students build a model of a two spring, single mass with fixed end configuration and then plot solutions to experience the motion.

    Keywords: massundampedFree Body Diagramspringstwo springsoscillationspring constantfixed ends

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    2014-Murillo-EtAl-Vertical Transmission in a Two-Strain Model of Dengue Fever
    The model is used to show that lower transmission rates of DENV-2 Asian are sufficient for displacing DENV-2 American in the presence of vertical transmission.

    Keywords: Peruvector-host modeldengueepidemmiologyvertical transmission

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    1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall
    We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.

    Keywords: fallingterminal velocityshuttlecockvertical fall

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